Let me tell you how the grocery stores in Italy are operating (I have relatives there):
First of all, you have to schedule a specific time slot to go shopping, to ensure that the store never gets too crowded. Secondly, you aren't allowed within two meters of anyone at any point. All of the store employees are wearing protective gear (gloves, masks, etc.). When you checkout, you push your cart up to them, they ring everything up, set it back down, and then you pack your bags yourself while they go away (to maintain a distance of two meters). They might be changing gloves with every checkout, too.
I have less knowledge of China, but I think it's similar. I saw a video of a ranged thermometer being used on every person before being allowed inside. Maybe Italy is doing similar. If and only if you have a fever or a confirmed infection then are you not allowed to leave your dwelling at all (unless it's to go to a hospital); that's when you get your food delivered.
With containment measures this drastic, you can definitely keep the infection rate below 1, which is all you need to stop an infection. And it's exactly these kinds of measures that need to be taken, because food is essential. You cannot have people starving to death en masse. Grocery stores are essential, and it's possible to allow grocery shipping while largely mitigating the spread of disease. Needless to say, all gatherings are banned, most stores are shut, and restaurants are to-go/delivery only (if they're even still open).
And I'm not drastically over-simplifying things, unless you somehow think that "shut down almost everything except for grocery stores and healthcare" is "over-simplified". This is working in China. They are stopping the spread of the disease while simultaneously maintaining access to food and healthcare.